Connectives in first-order logic sentences, Computer Engineering

Connectives in first-order logic sentences - Artificial intelligence

We may string predicates together into a sentence in the same way by utilising connectives that we did for propositional logic. We call a set of predicates strung together in the definite way a sentence. Notice that a particular predicate may be thought of as a sentence.

There are 5 connectives in first order logic. Firstly, we have "and", which we write ∧, and "or", which we write ∨. In the obvious ways these connect predicates together. So that if we wanted to say that "Simon lectures Artificial Intelligence and Simon lectures bioinformatics", we could write down:

lectures_ai(simon) ∧ lectures_bioinformatics(simon)

Notice also that now we are talking regarding different lectures, it must be a good idea to change our option of predicates, and make ai and bioinformatics constants:

lectures(simon, ai) ∧ lectures(simon, bioinformatics)

The other connectives existing to us in first-order logic are (a) "not", written that negates the truth of a predicate (b) "implies", written which may be used to say that 1 sentence being true follows from another sentence being true, and (c) "if and only if" (also known as "equivalence"), written ->, which may be used to state that the truth of 1 sentence is always the same as the truth of another sentence.

For example, if we want to say that "if Simon isn't lecturing Artificial Intelligence, then Bob might be lecturing AI", we could write it thus:

 ¬ lectures(simon, ai) -> lectures(bob, ai)

The things that predicates regard are terms: these may be variables, constants or the output from functions.

Posted Date: 10/2/2012 4:03:23 AM | Location : United States

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